After filing for bankruptcy, Houston Refining, L.P. (Houston Refining), suspended matching contributions to its employees’ 401(k) plans. The company later agreed to enter into arbitration regarding the suspension with the United Steel, Paper and Forestry, Rubber, Manufacturing, Energy, Allied Industrial and Service Workers International Union, acting on behalf of itself and its local unions (collectively Union). After the arbitrator found that the suspension violated the parties’ collective bargaining agreement, Houston Refining brought an action in the district court to vacate the arbitral award, and the Union counterclaimed to enforce the award. Both parties moved for summary judgment. The district court denied the company’s motion, granted the Union’s motion in part, and remanded to the arbitrator for clarification of the remedy. Houston Refining timely appealed. We reverse and remand.
I
Houston Refining operates a refinery on the east side of Houston. Many of its employees are members of the Union. In 2006, the Union and Houston Refining executed a collective bargaining agreement (2006 CBA). Ahead of the 2006 CBA’s scheduled expiration on January 31, 2009, the parties began negotiating a successor contract. When the negotiation stalled, they agreed to a twenty-four-hour rolling extension of the 2006 CBA (extension agreement), which could be cancelled with twenty-four hours’ notice.
Article 30 of the 2006 CBA establishes grievance and arbitration procedures, while Article 40 references various employee benefits. Article 30 defines a grievance as any difference regarding wages, hours or working conditions between the parties ... covered by this Agreement, 2006 CBA, art. 30, ¶ 1, and sets forth a grievance procedure that culminates in arbitration, id. art. 30, ¶ 7. Article 40 provides that employees are eligible to participate in various benefit plans. Among these plans is the 401K and Savings Plan for Represented Employees, id. art. 40, pt. Ill, *399¶ 1(e) (401(k) Plan), administered by the Benefits Administrative Committee. Article 40 further provides that the Company will provide advance notice of proposed changes to the benefit plans, after which the Union will have [a] reasonable time period ... to elect inclusion in or exclusion from the amended benefits plan. Id. art. 40, pt. Ill, ¶ 5.
According to Houston Refining negotiators, the Union negotiator informed them that the extension agreement would expire upon ratification of a successor CBA. In February 2009, the parties’ negotiators reached a tentative agreement on a new CBA (2009 CBA), which the Union’s local membership ratified by majority vote days later. However, the Union subsequently refused to sign the 2009 CBA after a disagreement arose over certain terms. The parties now agree that the 2009 CBA never took effect.1
In March 2009, having filed for Chapter 11 bankruptcy in the Southern District of New York, Houston Refining informed the Union that it would suspend its matching contributions to employees’ 401(k) plans.2 Although the Union representative did not mention an exclusion from the plan amendment, he responded, Well you know I’m going to have to sue you. Houston Refining proceeded to eliminate the matching contributions by means of an amendment to the 401(k) Plan.
After the suspension came into effect, the Union filed a grievance with Houston Refining, demanding that the company resume matching contributions and compensate employees for any unpaid contributions. The text of the grievance quoted from the 2009 CBA, rather than the 2006 CBA. Houston Refining refused to process the grievance, claiming that the suspension was not a grievable issue. Months later, the Union commenced an adversary proceeding in the bankruptcy court to compel Houston Refining to arbitrate the grievance under the 2009 CBA. The complaint was amended to allege that, in the alternative, the 2006 CBA mandated arbitration.
The parties then concluded the Settlement Agreement to submit the grievance to arbitration, which the bankruptcy court approved. The Settlement Agreement provided in relevant part:
1. The parties agree to proceed to arbitration with the grievances [regarding 401(k) matching contributions] expeditiously and in compliance with the arbitration procedures ... in the applicable collective bargaining agreements. [¶]... ]
4. At arbitration, the parties shall reserve all rights to present any and all arguments and advance any and all defenses to them including, without limitation, arguments concerning whether or not an applicable collective bargaining agreement was in effect at the time that a particular grievance arose.
Settlement Agreement, ¶¶ 1, 4. Pursuant to the terms of the Settlement Agreement, the parties entered into arbitration.
*400Following a two-day hearing, Arbitrator Charles G. Griffin rendered an award in favor of the Union. The arbitrator found that the 2006 CBA, by way of the extension agreement, was in effect when the Union filed its grievance and that the grievance was an arbitrable dispute over wages under that CBA’s arbitration clause because the matching contributions had monetary value. He also found immaterial the fact that the grievance quoted from the 2009 CBA. Lastly, he concluded that Houston Refining violated Article 40 of the 2006 CBA by unilaterally amending the 401(k) Plan, because the Union had effectively elected exclusion from the amendment when it expressed intention to sue over the suspension.
Houston Refining filed suit in the district court seeking to vacate the arbitral award under section 301 of the Labor Management Relations Act, 29 U.S.C. § 185, and the Union counterclaimed to enforce the award. Both parties moved for summary judgment. The district court found that because the Settlement Agreement evinced the parties’ clear agreement to have the arbitrator decide questions of arbitrability, its review of this issue would be deferential. The district court then upheld the arbitrability determinations— that the 2006 CBA existed when the grievance was filed, and that the arbitrator acted within his authority under that CBA’s arbitration clause. On the merits, the district court upheld the arbitrator’s finding that Houston Refining violated Article 40 of the 2006 CBA, but concluded that the arbitral award’s remedy was ambiguous in certain respects. The district court accordingly denied the company’s motion and granted the Union’s motion in part,3 but remanded to the arbitrator for clarification of the award’s monetary value, among other issues. Houston Refining timely appealed.
II
Questions of subject-matter jurisdiction are reviewed de novo. Wagner v. United States, 545 F.3d 298, 300 (5th Cir.2008). Subject-matter jurisdiction cannot be forfeited or waived and should be considered when fairly in doubt. Ashcroft v. Iqbal, 556 U.S. 662, 671, 129 S.Ct. 1937, 173 L.Ed.2d 868 (2009); see also Steel Co. v. Citizens for a Better Env’t, 523 U.S. 83, 94-95, 118 S.Ct. 1003, 140 L.Ed.2d 210 (1998).
This court reviews a district court’s grant of summary judgment de novo. Resolution Performance Prods., LLC v. Paper Allied Indus. Chem. & Energy Workers Int’l Union, Local 1-1201, 480 F.3d 760, 764 (5th Cir.2007).
III
Houston Refining first contends that the existence of an applicable CBA is necessary for subject-matter jurisdiction under section 301 of the Labor Management Relations Act, 29 U.S.C. § 185. The company further claims that courts can assume jurisdiction to address the merits when factual issues are common to both, and that in this case, the CBA’s existence is precisely such a common factual issue— without an existing CBA, the Union’s grievance would not be arbitrable.4 Thus, *401in Houston Refining’s view, we must remand to allow the district court to determine whether a CBA existed, and if it decides in the negative, it could vacate the arbitral award on the grounds that the parties never agreed to arbitrate the dispute.
A
The first question is whether, under section 301(a), the existence of a labor contract is a requirement for federal subject-matter jurisdiction, as Houston Refining submits. Relatedly, we ask if anything less would be sufficient to support such jurisdiction. Section 301(a) provides:
Suits for violation of contracts between an employer and a labor organization representing employees in an industry affecting commerce as defined in this chapter, or between any such labor organizations, may be brought in any district court of the United States having jurisdiction of the parties, without respect to the amount in controversy or without regard to the citizenship of the parties.
29 U.S.C. § 185(a). If the existence of a contract were jurisdictional, then because the district court’s subject-matter jurisdiction would be fairly in doubt, this Court (or the district court on remand) would be obligated to confirm this jurisdiction. Iqbal, 556 U.S. at 671, 129 S.Ct. 1937. By contrast, if section 301(a) were not jurisdictional, then here, the question of the CBA’s existence would be subsumed within the broader issue of whether the parties agreed to arbitrate the Union’s grievance. See infra Part IV.B. (discussing arbitrability questions).
We have in the past read section 301(a) as a jurisdictional requirement. In Alexander v. International Union of Operating Engineers, AFL-CIO, 624 F.2d 1235 (5th Cir.1980), an international union directed its local union’s officer to sign a project agreement previously rejected by the local’s membership. Two individual local union members sued the unions for money damages under section 301, alleging a violation of the international union’s constitution. Id. at 1236-37. The district court denied relief as to this claim on jurisdictional grounds. Id. at 1237,1239.5
We first explained that [t]he issue of whether individual union members may use section 301 as a jurisdictional basis to sue their 'local or international unions is a matter of first impression in this Circuit. Id. at 1238. We then prefaced our analysis by observing that [a]s the language in section 301 makes clear, jurisdiction depends on whether there is a contract between an employer and a labor organization or between two labor organizations. Id. Following many sister circuits, we held that in order for section 301(a) jurisdiction to reach suits for violations of union constitutions, the alleged violation must create a threat to industrial peace or have a significant impact upon labor-employer relations. Id. We reasoned that, in contrast to cases from other circuits where a genuine impact on industrial peace had been adequately alleged, id., [w]ith respect to [the parent union constitution] and that alleged violation, plaintiffs have not shown there was any real threat to industrial peace or any *402significant impact on the relationship with the employer, id. at 1239. Accordingly, we concluded that the district court properly denied jurisdiction under [section 301]. Id.6
Importantly, our statement in Alexander that jurisdiction depends on whether there is a contract merely acknowledged the presence of the term contracts in the statutory language. Id. at 1238. Nowhere did we require factual proof of a labor contract’s existence, and our reasoning bears out our central concern: The plaintiffs did not even allege a contractual violation covered by section 301(a), as they failed to claim that the international union constitution was a contract whose violation create[d] a threat to industrial peace or ha[d] a significant impact upon labor-employer relations. Id.7
Alexander, then, establishes that an allegation of a contractual violation is necessary for section 301(a) jurisdiction. But we had no occasion to decide whether such an allegation was sufficient for such jurisdiction. As particularly relevant to this case, Alexander did not consider whether, if an allegation of a contract’s existence is later challenged and disproven as a factual matter, section 301(a) jurisdiction could still reach such a case. See Jolly Op. at 399.
The Supreme Court subsequently answered this question: An allegation of a labor contract violation is sufficient to support subject-matter jurisdiction under section 301(a). See Textron Lycoming Reciprocating Engine Div., AVCO Corp. v. United Auto., Aerospace & Agric. Implement Workers of Am., Int’l Union, 523 U.S. 653, 657-58, 118 S.Ct. 1626, 140 L.Ed.2d 863 (1998). In Textron, a union sought a declaratory judgment that its CBA with Textron was voidable. Id. at 654-55, 118 S.Ct. 1626. The union alleged] that Textron had fraudulently in*403duced the CBA’s execution, but [did] not allege that either it or Textron ever violated the [CBA]. Id. at 655, 118 S.Ct. 1626. The district court dismissed for lack of subject-matter jurisdiction under section 301(a), and the court of appeals reversed. Id. at 656, 118 S.Ct. 1626.
In reversing the court of appeals, the Supreme Court first explained that section 301(a) confers federal subject-matter jurisdiction only over ‘[s]uits for violation of contracts,’ id. at 656, 118 S.Ct. 1626, and that as a textual matter, such suits do not include suits that claim a contract is invalid, id. at 657, 118 S.Ct. 1626. The Court then explained:
This does not mean that a federal court can never adjudicate the validity of a contract under § 301(a). That provision simply erects a gateway through which parties may pass into federal court; once they have entered, it does not restrict the legal landscape they may traverse. Thus if, in the course of deciding whether a plaintiff is entitled to relief for the defendant’s alleged violation of a contract, the defendant interposes the affirmative defense that the contract was invalid, the court may, consistent with § 301(a), adjudicate that defense.
Id. at 657-58, 118 S.Ct. 1626. In closing, the Court reasoned that [sjection 301(a) jurisdiction does not lie over such a case because the union neither alleges that Tex-tron has violated the contract, nor seeks declaratory relief from its own alleged violation. Id. at 658, 118 S.Ct. 1626; see also id. at 661-62, 118 S.Ct. 1626 (restating same conclusion).
Textron thus teaches that an alleged violation satisfies section 301(a)’s jurisdictional requirement. Id. at 658, 118 S.Ct. 1626 (emphasis added). The Court’s hypothetical adjudication] of the affirmative defense of a labor contract’s invalidity would require a disposition on the merits of that defense, not on jurisdictional grounds, since the parties would have already passed through the jurisdictional gateway ... into federal court. Id. at 658, 118 S.Ct. 1626 (emphasis added).8 This principle complements our analysis in Alexander, and reading the two cases together yields the conclusion that an allegation of a labor contract violation is both necessary and sufficient to support subject-matter jurisdiction under section 301(a).9 If the court later finds the allegedly violated contract to be non-existent or invalid, it must dismiss for failure to state a claim, not for lack of jurisdiction.10
To be sure, neither Alexander nor Tex-tron implicated arbitration, as this case does. But no authority supports the proposition that arbitration alters those cases’ teachings on the jurisdictional requirement of section 301 (a) — that a party alleging a labor contract violation passes through the statute’s jurisdictional gateway. Id. Indeed, the Supreme Court has previously treated an agreement to arbitrate as any *404other labor contract whose alleged violation is actionable under section 301(a). See Atkinson v. Sinclair Refining Co., 370 U.S. 238, 241, 82 S.Ct. 1318, 8 L.Ed.2d 462 (1962) (The Congress has by [section] 301 of the Labor Management Relations Act, assigned the courts the duty of determining whether the reluctant party has breached his promise to arbitrate, (citation omitted)).
Houston Refining urges us to reject the Third and Sixth Circuits’ approach of treating the factual existence of a labor contract as an element of a plaintiffs claim and instead follow the Eighth Circuit, which recognizes the jurisdictional nature of section 301(a). Compare Winnett v. Caterpillar, Inc., 553 F.3d 1000, 1007 (6th Cir.2009); Pittsburgh Mack Sales & Serv., Inc. v. Int’l Union of Operating Eng’rs, Local Union No. 66, 580 F.3d 185, 189-90 (3d Cir.2009), with ABF Freight Sys., Inc. v. Int’l Bhd. of Teamsters, 645 F.3d 954, 961-64 (8th Cir.2011). The Third and Sixth Circuits relied on Arbaugh v. Y & H Corp., 546 U.S. 500, 126 S.Ct. 1235, 163 L.Ed.2d 1097 (2006), in which the Supreme Court explained that when Congress does not rank a statutory limitation on coverage as jurisdictional, courts should treat the restriction as non-jurisdictional in character. Id. at 516, 126 S.Ct. 1235. In ABF Freight, the Eighth Circuit explained that the Third and Sixth Circuits, in interpreting Arbaugh, did not have the benefit of the Supreme Court’s subsequent discussion in Henderson ex rel. Henderson v. Shinseki, 562 U.S. 428, 131 S.Ct. 1197, 179 L.Ed.2d 159 (2011). The Henderson Court, after reviewing Arbaugh’s bright line rule, explained that [w]hen a long line of [the] Court’s decisions left undisturbed by Congress has treated a similar requirement as jurisdictional, [the Court] will presume that Congress intended to follow that course. Id. at 1203 (internal citation and quotation marks omitted). Applying Henderson, the Eighth Circuit reviewed several earlier Supreme Court cases on section 301(a) including Textron, all of which treated allegations of a labor contract violation as a jurisdictional requirement. See ABF Freight System, 645 F.3d at 961-64 (reviewing cases). Accordingly, the court concluded that section 301(a) is jurisdictional. Id. at 963.
But neither the Third, Sixth, nor Eighth Circuits contemplated whether an alleged labor contract violation can support federal subject-matter jurisdiction under section 301(a). The Third and Sixth Circuits are correct insofar as they hold that factual proof of a labor contract is not necessary for such jurisdiction, and that if a court finds that such a contract is invalid, it should dismiss for failure to state a claim. See Textron, 523 U.S. at 658, 118 S.Ct. 1626. But those decisions did not recognize that under Textron, section 301(a) jurisdiction requires an alleged labor contract violation.11 The Eighth Circuit, for its part, correctly holds that section 301(a) is jurisdictional, but ABF Freight does not clearly explain what suffices for obtaining such jurisdiction.12 Accordingly, the juris*405dictional question in this case is best resolved by Alexander and Textron, rather than any decision of our sister circuits.
Lastly, section 301(a) jurisdiction cannot be so permissive as to reach any action filed because a contract has been violated, Higginson Op. at 420 (quoting Textron, 523 U.S. at 657, 118 S.Ct. 1626), or any suit ... to vacate an arbitral decision finding that the plaintiff violated a CBA, id. at 420. These propositions would side-step Textron’s copious references to the union’s failure in that case to allege any violation of the CBA. See Textron, 523 U.S. at 655, 658, 661-62, 118 S.Ct. 1626.13 Nor could section 301(a) jurisdiction reach any controversies involving collective-bargaining agreements. Higginson Op. at 420 (quoting Lingle v. Norge Division of Magic Chef, Inc., 486 U.S. 399, 403, 108 S.Ct. 1877, 100 L.Ed.2d 410 (1988)). In Lingle, the Supreme Court did mention that certain controversies involving CBAs fall within section 301 jurisdiction, summarizing its earlier holding in Textile Workers Union of Am. v. Lincoln Mills of Ala., 353 U.S. 448, 77 S.Ct. 912, 1 L.Ed.2d 972 (1957). But Lincoln Mills confirmed section 301 jurisdiction not for any disputes merely implicating CBAs, but rather cases involving alleged labor contract violations, in which parties had sought enforcement of those contracts — namely, the performance of promises to arbitrate grievances under [CBAs]. Lincoln Mills, 353 U.S. at 451, 77 S.Ct. 912 (emphasis added), accord Lingle, 486 U.S. at 403, 108 S.Ct. 1877; see also Sinclair Refining Co., 370 U.S. at 241, 82 S.Ct. 1318.14 Furthermore, to allow any suit merely involving a CBA — even lacking an alleged violation — would run afoul of Textron. After all, the Textron Court held that section 301 jurisdiction did not reach a suit involving a CBA’s voidability because the complaint did not allege a CBA violation.15
Under Textron and Alexander, the alleged violation of a labor contract is both necessary and sufficient to invoke federal subject-matter jurisdiction under section *406301(a) of the Labor Management Relations Act, 29 U.S.C. § 185(a). See Textron, 523 U.S. at 657-58, 118 S.Ct. 1626; Alexander, 624 F.2d at 1238.
B
Because a party need only allege the violation of a labor contract to invoke federal subject-matter jurisdiction under section 301, this requirement was easily satisfied here.
This suit involves at least two alleged violations of a labor contract. First, Houston Refining’s complaint claimed that the Union alleged the company had violated a CBA.16 Second, in requesting vacatur of the arbitral award, Houston Refining alleged that the award violated the terms of the 2006 CBA — assuming arguendo its existence.17 Accordingly, the district court properly exercised subject-matter jurisdiction over this suit for violation of contracts between an employer and a labor organization. 29 U.S.C. § 185(a).18
Additionally, because section 301’s jurisdictional requirement does not require factual proof of a valid labor contract, Houston Refining’s collateral attack on ar-bitrability is meritless. Houston Refining relies on Montez v. Department of the Navy, 392 F.3d 147 (5th Cir.2004), for the proposition that where issues of fact are central both to subject matter jurisdiction and the claim on the merits, ... the trial court must assume jurisdiction and proceed to the merits. Id. at 150. By Houston Refining’s logic, because the merits of this appeal concern whether the grievance was arbitrable, and because the parties agree that a valid CBA was necessary for such arbitrability, the question of the CBA’s existence is common to both jurisdiction and the merits. See infra Part IV.B. Thus, the company does not ask the district court to dismiss for lack of jurisdiction — for dismissal would allow the ar-bitral award to stand.19 Rather, invoking Montez, Houston Refining apparently *407views this jurisdictional claim as an alternative path for the district court to vacate the award on arbitrability grounds, a path that would conveniently elide the question of whether the parties agreed to give arbi-trability to the arbitrator. See infra Part IV.A.
But Montez’s interpretation of the Federal Tort Claims Act is inapplicable because as explained above, under Textron, the jurisdictional issue under section 301(a) does not hinge on issues of fact, but rather on allegations of a contract violation. Montez, 392 F.3d at 150. That is, under section 301(a), the jurisdiction and arbitrability inquiries are not factually intertwined. Id. Accordingly, Montez cannot permit the district court to assume jurisdiction in order to resolve the arbitra-bility question de novo.20
Because Houston Refining’s complaint alleges both that the Union claimed the company violated a CBA, and that the arbitral award violates the 2006 CBA, the district court had subject-matter jurisdiction under section 301(a) of the Labor Management Relations Act, 29 U.S.C. § 185(a).21
IV
Houston Refining next contends that the district court erred in deferring to the arbitrator’s determination of the grievance’s arbitrability. According to the company, because the parties never agreed in clear and unmistakable terms to give the issue of arbitrability to the arbitrator, the district court was obligated to decide the issue independently. Houston Refining further urges us to resolve certain disposi-tive arbitrability questions on appeal and render judgment in its favor.
[JJudicial review of an arbitration award arising from the terms of a CBA is narrowly limited as to the merits of the award. Albemarle Corp. v. United Steel Workers, 703 F.3d 821, 824 (5th Cir.2013) (citation and internal quotation marks *408omitted).22 By contrast, the law presumes that courts have plenary power to decide the gateway question of a dispute’s arbi-trability — i.e., whether [the parties] agreed to arbitrate the merits. First Options of Chi., Inc. v. Kaplan, 514 U.S. 938, 942, 115 S.Ct. 1920, 131 L.Ed.2d 985 (1995).
When a party calls upon a court to decide a dispute’s arbitrability, the court must determine whether the dispute falls within the ambit of the parties’ agreement to arbitrate. [Arbitration is simply a matter of contract between the parties; it is a way to resolve those disputes — but only those disputes — that the parties have agreed to submit to arbitration. First Options, 514 U.S. at 943, 115 S.Ct. 1920. If the parties did not so agree, then the party who has not agreed to arbitrate will normally have a right to a court’s decision about the merits of its dispute. Id. at 942, 115 S.Ct. 1920.
Yet like any other disputed issue, even the gateway question of arbitra-bility can be given to an arbitrator, if the parties so choose. But the party contending that an arbitrator has authority to decide arbitrability bears the burden of demonstrating clearly and unmistakably that the parties agreed to have the arbitrator decide that threshold question.... ConocoPhillips, Inc. v. Local 13-0555 United Steelworkers Int’l Union, 741 F.3d 627, 630 (5th Cir.2014) (citation and internal alteration omitted). [M]erely arguing the arbitrability issue to an arbitrator does not indicate a clear willingness to arbitrate that issue, i.e., a willingness to be effectively bound by the arbitrator’s decision on that point. First Options, 514 U.S. at 946, 115 S.Ct. 1920. Nor do ambiguity and silence suffice. ConocoPhillips, 741 F.3d at 632. If the party cannot carry its burden, then the court should decide [the arbitrability] question just as it would decide any other question that the parties did not submit to arbitration, namely, independently. Id. at 630 (quoting First Options, 514 U.S. at 943, 115 S.Ct. 1920).23
A
We first consider whether, on the undisputed facts at summary judgment, the Union carried its burden of proving that the parties clearly and unmistakably agreed to have the arbitrator decide arbi-trability. ConocoPhillips, 741 F.3d at 630. Absent such proof, the district court had to decide arbitrability independently.24 The *409Union submits that the parties expressed agreement to arbitrate arbitrability both by their conduct in arbitration proceedings and by the Settlement Agreement, and we consider each in turn below.25
As for their conduct at arbitration, the parties agree that Houston Refining argued at length about arbitrability before the arbitrator. But merely arguing the arbitrability issue to an arbitrator does not indicate a clear willingness to arbitrate that issue. First Options, 514 U.S. at 946, 115 S.Ct. 1920. The Union does not dispute this well-established rule or advance any other reason why the arbitration proceedings demonstrated any agreement to arbitrate arbitrability.
The Settlement Agreement is also unavailing because its terms are too ambiguous to evince a clear and unmistakable agreement to arbitrate arbitrability. This ambiguity is borne out by the parties’ plausible but conflicting interpretations. Houston Refining contends that it did not agree to give the arbitrator the final word on arbitrability, citing this clause:
At arbitration, the parties shall reserve all rights to present any and all arguments and advance any and all defenses to them including, without limitation, arguments concerning whether or not an applicable collective bargaining agreement was in effect at the time that a particular grievance arose.
Settlement Agreement, ¶ 4. The company explains that, in particular, the words shall reserve demonstrate that the parties contemplated potential judicial review, especially on the matter of arbitrability, which encompasses the factual inquiry into whether or not an applicable collective bargaining agreement was in effect at the time that a particular grievance arose. Id. In Houston Refining’s view, the Union effectively construes reserve to mean exhaust. The Union does not refute this reading, but points to another clause in the Agreement stating that the parties agree[d] to proceed to arbitration with the grievances [regarding 401(k) contributions] expeditiously and in compliance with the arbitration procedures ... in the applicable collective bargaining agreements. Id. ¶ 1. While these provisions seem to be in tension, the Union proffers nothing more.26
The Union additionally contends that allowing Houston Refining to return to the courts would result in a waste of judicial *410resources ... [that] the policy of deference to arbitral awards intends to avoid.27 Houston Refining, for its part, acknowledges that under its reading, the Settlement Agreement inverts the usual timing: The parties forgo an initial court decision about arbitrability but, following arbitration, are able to litigate about arbitrability and other issues in court. Yet the Supreme Court in First Options rejected the same concerns about delay and waste and concluded that factual circumstances vary too greatly to permit a confident conclusion about whether allowing the arbitrator to make an initial (but independently reviewable) arbitrability determination would, in general, slow down the dispute resolution process. First Options, 514 U.S. at 946-47, 115 S.Ct. 1920. Thus, the First Options default rule that courts decide arbitrability absent clear agreement avoids case-by-case weighing of costs and benefits, and strikes a desirable balance between reaping the efficiencies of arbitration and ensuring access to judicial review on the rather arcane question of who decides arbitrability, which parties reasonably would have thought a judge, not an arbitrator, would decide. See id. at 945, 115 S.Ct. 1920 (citation omitted).
In light of the parties’ ambiguity and silence, ConocoPhillips, 741 F.3d at 632, the Union has not carried its burden of establishing that the parties clearly and unmistakably agreed to arbitrate arbitra-bility, id. at 630.28 Accordingly, we hold that the district court erred as a matter of law in failing to decide arbitrability just as it would decide any other question that the parties did not submit to arbitration, namely, independently. Id.
B
We decline today to decide whether the Union’s grievance was arbitrable. This appeal presents three distinct arbitrability inquiries, and the district court is better positioned to assess the parties’ arguments in the first instance and develop the record as necessary.
The first arbitrability inquiry is whether the 2006 CBA existed when the Union filed its grievance. The parties seem to agree that if no CBA was in effect at all, then arbitration would be unavailable. This ar-*411bitrability question also appears to be the most fact-intensive one, and neither party asks us to decide it on the limited record before us.
The second and third arbitrability inquiries concern whether,, even if the 2006 CBA existed, the arbitrator exceeded his authority under that CBA. Houston Refining urges us to hold that the arbitrator did exceed his authority and vacate the award — on either of two independent grounds. First, the company contends that the Union’s grievance quoted the text of the 2009 CBA, such that the grievance is invalid under the 2006 CBA’s arbitration clause. See 2006 CBA, art. 30, ¶¶ 1, 7(b). Additionally, Houston Refining submits that its unilateral suspension of the 401(k) Plan, allegedly in violation of Article 40 of the 2006 CBA,29 does not concern wages within the meaning of the CBA’s arbitration clause. See id. art. 30, ¶ 1.
We reserve these and all other arbitra-bility questions for the district court, which must on remand decide the grievance’s arbitrability independently, without deference to the arbitral decision. ConocoPhillips, 741 F.3d at 630.
C
Judge Higginson, in dissent, would vacate the arbitral award on the grounds that the arbitrator exceeded his authority because the term wages in the CBA’s arbitration clause cannot encompass this dispute over the 401(k) match suspension. Although we do not decide any question of arbitrability, given the important doctrinal questions raised by the dissent, we here explain why we would disagree, at least on this record.
1
The dissent errs in construing Houston Refining’s claim about the scope of the CBA’s arbitration clause as a claim that the arbitrator exceeded his powers, rather than a challenge to the dispute’s arbitra-bility.
Under its assumptions,30 the dissent reasons that we would have authority to construe the scope of the 2006 CBA’s arbitration clause because we may always decide whether the arbitrator exceeded] his contractual mandate, Beaird Indus., Inc. v. Local 2297, Int’l Union, 404 F.3d 942, 946 (5th Cir.2005), and because, here, Houston Refining contends that the arbitrator exceeded his powers by treating a 401(k) dispute as grievable.
But Houston Refining has not established an excess-of-powers challenge under Beaird. In Beaird, we considered a party’s challenge to an arbitrator’s mandate to decide the merits, where arbitrability was undisputed. Beaird, 404 F.3d at 943. Unlike Beaird, Houston Refining does not contend that the arbitrator exceeded his mandate to decide the merits. In fact, Houston Refining correctly observes that the merits are not here at all on this appeal; it does not challenge the arbitrator’s finding that the unilateral 401 (k) *412match suspension violated Article 40 of the CBA. Nor does Houston Refining demonstrate that the arbitrator exceeded his mandate to decide arbitrability — by ignoring unambiguous, express contractual provisions prohibiting arbitration of the Union’s grievance. Beaird, 404 F.3d at 946.
Rather, Houston Refining’s contention— that the parties’ agreement to arbitrate does not cover the Union’s grievance— concerns a quintessential question of the dispute’s arbitrability. Supra Part IV.B.31 To be sure, Houston Refining deploys the phrase exceeded his powers and cites Beaird. But this is nothing more than an attempt to transform an arbitrability claim into an excess-of-powers claim, thus preserving an alternate grounds for vacatur. Indeed, we have routinely construed claims that an arbitral body exceeded its powers by issuing an award on a claim not covered by the parties’ arbitration agreement as raising a question of arbitra-bility. Petrofac, Inc. v. DynMcDermott Petroleum Operations Co., 687 F.3d 671, 674 (5th Cir.2012) (emphasis added); see also Downer v. Siegel, 489 F.3d 623, 626-27 (5th Cir.2007) (same). Tellingly, both parties’ leading cases on whether certain disputes implicating benefits are covered by arbitration clauses all invoke the presumption of arbitrability; therefore, this case, like those, presents a question of arbitrability. See infra Part IV.C.2 (reviewing cases).
The dissent wants to have it both ways: Even if we were to find that the parties agreed clearly and unmistakably to arbitrate arbitrability, we would retain the power to vacate the award for lack of arbitrability. But our law forbids such a procedure.
2
Because we would hold that the parties here did not clearly and unmistakably agree to arbitrate arbitrability, see supra Part IV.A., the courts must decide arbitra-bility questions independently.
But this independent inquiry is circumscribed by a presumption favoring arbitrability: [W]here the contract contains an arbitration clause, there is a presumption of arbitrability. AT & T Techs., Inc. v. Commc’ns Workers of Am., 475 U.S. 643, 650, 106 S.Ct. 1415, 89 L.Ed.2d 648 (1986). That presumption applies unless it may be said with positive assurance that the arbitration clause is not susceptible of an interpretation that covers the asserted dispute. Doubts should be resolved in favor of coverage. Id. However, the policy that favors resolving doubts in favor of arbitration cannot serve to stretch a contractual clause beyond the scope intended by the parties or authorize an arbiter to disregard or modify the plain and unambiguous provisions of the agreement. Smith v. Transp. Workers Union of Am., AFL-CIO Air Transport Local 556, 374 F.3d 372, 375 (5th Cir.2004) (citation and internal quotation marks omitted).32
*413Even undertaking an independent review of arbitrability under the 2006 CBA, assuming the CBA existed, we would not conclude on this record that because this dispute does not concern wages, vacatur is proper.
The dissent’s analysis of the 2006 CBA says nothing about whether it may be said with positive assurance that the arbitration clause is not susceptible of an interpretation that covers the asserted dispute. AT & T, 475 U.S. at 650, 106 S.Ct. 1415 (emphasis added). That is, we have no license to interpret the CBA de novo; rather, we must ask whether any interpretation could bring this dispute within the ambit of the arbitration clause, bearing in mind that [d]oubts should be resolved in favor of coverage. Id. Here, Arbitrator Griffin concluded that the dispute was ar-bitrable, explaining that because matching contributions had monetary value, they could be considered a form of wages, and that the match suspension violated an express provision of the CBA — Article 40, which governed procedures for amending the 401(k) Plan.
The case law makes the CBA particularly susceptible of the arbitrator’s interpretation. Id.33 First, this case can be distinguished from our decision in Local Union No. 4-449, Oil, Chem. & Atomic Workers Union v. Amoco Chem. Corp., 589 F.2d 162 (5th Cir.1979). At issue in Amoco were two grievances filed by [union] members ... contesting the denial of sick pay benefits for certain work absences. Id. at 163. We concluded that a process for obtaining sickness and disability benefits, expressly constructed by the CBA and benefits plan, sufficiently exclude[d] arbitration for grievances concerning sickness and disability benefits. Id. at 164. We relied on the fact that under the CBA, Amoco’s Board of Directors had the right to interpret and apply the [Benefits] Plan, and that their decision would be final. Id. Thus, the two grievances fell squarely within the jurisdiction of the Board of Directors.
*414In contrast to Amoco, this case does not involve individual Union members’ challenges to the denial of their benefits under the IpOlQc) Plan — the purview of Houston Refining’s Benefits Administrative Committee. Rather, the Union alleges that the procedure by which Houston Refining amended the 401 (k) Plan violated its obligations under the 2006 CBA The record before us indicates that the Committee is charged only with the administration of the 401(k) Plan — including the power to construe and interpret all Plan terms and to determine all controversies relating to Plan administration. Had Union members sought to enforce their rights under the 401(k) Plan, then the Committee could certainly interpret and apply that Plan. Amoco, 589 F.2d at 164. But Houston Refining has not proffered any evidence showing that the Committee, in the course of administering the 401(k) Plan, can determine whether that Plan was lawfully amended under the 2006 CBA. In fact, Houston Refining has suggested precisely the opposite: Because the 401(k) Plan expressly permits the company to make unilateral amendments at any time and from time to time, the Committee, in carrying out its duty of applying the Plan’s terms, would likely never be able to recognize a breach of Article 40 of the 2006 CBA.34
Our sister circuits’ decisions also support an interpretation of the 2006 CBA favoring arbitrability. To be sure, the Third and Seventh Circuits found that arbitration of a benefits-related grievance was unavailable where arbitration clauses covered only disputes over wages, hours, or working conditions, like the clause here. Higginson Op. at 424. But those decisions turned not on the scope of wages,35 but on the fact that the CBA was not the source of the allegedly violated right.36 Elsewhere, under arbitration clauses facially broader than the one at issue here, the Fourth and Seventh Circuits concluded that disputes were arbitrable.37 But other courts, notwithstanding similarly broad clauses, concluded that disputes were not arbitrable — again, because the right at issue was protected by a separate benefits grievance procedure.38
In sum, Amoco and our sister circuits’ decisions could be read to stand for this *415proposition: A dispute is arbitrable if the dispute concerns a direct violation of a right under the CBA, rather than a challenge to a determination of an employee’s eligibility for benefits under the benefits plan. This principle recognizes the importance of the source of the disputed right, and, furthermore, prevents clashes between arbitration and disputes governed by the Employee Retirement Income Security Act (ERISA), about which Houston Refining professes to be concerned. Compare Amoco, 589 F.2d at 164 (holding dispute over two employees’ entitlement to sick pay benefits not arbitrable and explaining that Board of Directors has right to interpret and apply the [Sickness and Disability Benefits] Plan), with Printing Specialties & Paper Products Union Local 680, Graphic Commc’n Int’l Union, AFL-CIO v. Nabisco Brands, Inc., 883 F.2d 102, 105 (7th Cir.1987) (concluding that employee-specific benefits dispute was not arbi-trable under clause covering wages, hours or working conditions, but explaining that CBA violation would be arbitrable if Nabisco had violated an obligation under the [CBA] that abrogated the full force and effect of the [Benefits] Plan).39
Accordingly, if the 2006 CBA in fact existed, the case law applied to this record — under the presumption of arbitrability — demonstrates that the CBA’s arbitration clause is at least susceptible of an interpretation that would not bar arbitration of this dispute. AT & T, 475 U.S. at 650, 106 S.Ct. 1415.40
V
For the foregoing reasons, we REVERSE the judgment of the district court and REMAND for further proceedings.41
. In 2009, Houston Refining filed a complaint with the National Labor Relations Board (NLRB), alleging that the Union unlawfully refused to execute an agreed-upon CBA. The NLRB concluded that because there was no meeting of the minds on all substantive issues and material terms, Intermountain Rural Elec. Ass’n, 309 NLRB 1189, 1192 (1992), the 2009 CBA never came into effect. The parties do not dispute this determination. Eventually, in January 2010, the parties executed a new CBA, which is irrelevant to this appeal.
. Houston Refining filed for bankruptcy along with other subsidiaries and affiliates of Lyon-dell Chemical Company. Nothing in the record suggests that the bankruptcy court ordered the match suspension.
. The district court denied the Union’s request for attorney’s fees. This issue is not before us on appeal.
. Technically, the merits of this dispute concern whether Houston Refining’s 401 (k) match suspension violated Article 40 of the 2006 CBA, not whether the Union’s grievance is arbitrable. But below, in Part III.B. only, the term merits refers to the arbitrability issue, as distinguished from the jurisdictional question. See First Options of Chi., Inc. v. Kaplan, 514 U.S. 938, 942, 115 S.Ct. 1920, 131 L.Ed.2d 985 (1995) (distinguishing be*401tween three issues of merits, arbitrability, and who decides arbitrability).
. The district court granted relief only as against the local union under its duty of fair representation, which issue is not relevant to this case. Alexander, 624 F.2d at 1237. As for the section 301 claim, we presume that the district court dismissed for lack of jurisdiction, given that we affirmed on this issue and concluded that the district court properly denied jurisdiction under [section 301], Id. at 1239.
. We undertook a similar analysis in determining whether plaintiffs’ complaint was sufficient to confer jurisdiction under section 102 of the Labor Management Reporting and Disclosure Act, 29 U.S.C. § 412. Alexander, 624 F.2d at 1239-40. This section allows district courts to hear actions for violations of, among other provisions, section 101(a) of the Act, which provides that [ejvery member of a labor organization shall have equal rights and privileges with such organization.... 29 U.S.C. § 411(a)(1). Plaintiffs contended that the unions denied their right to vote by mandating the ratification of the rejected project agreement. Alexander, 624 F.2d at 1239. We explained that [tjhere is no allegation here that the two complaining union members have been discriminated against, or that they have been denied a privilege or right to vote that the union has granted to others. Id. at 1240; see also id. at 1241 (concluding that plaintiffs’ allegations of discrimination were sufficient) (Clark, J., concurring in part and dissenting in part).
. See also Wooddell v. Int’l Bhd. Of Elec. Workers, Local 71, 502 U.S. 93, 98-99, 112 S.Ct. 494, 116 L.Ed.2d 419 (1991) (No employer-union contract is involved here; if the District Court had § 301 subject-matter jurisdiction over petitioner’s suit against his union, it is because his suit alleges a violation of a contract between two unions, and because § 301 is not limited to suits brought by a party to that contract .... (emphasis added) (internal citations omitted)); id. at 98 n. 3, 112 S.Ct. 494 (explaining that district courts have jurisdiction over suits by a union member against his union for a violation of the union constitution only if it is charged that the breach alleged violates a contract between two labor organizations (emphasis added)).
Houston Refining misunderstands Carpenters Local Union No. 1846 v. Pratt-Farnsworth, Inc., 690 F.2d 489 (5th Cir.1982). There, a union sued two trade associations that lacked any contractual relationship with the union, but that allegedly conspired to effect their member companies' breaches of their labor contracts with the union. We held that because the plaintiff could not even allege that the defendants were parties to a labor contract, jurisdiction under section 301 was lacking. Id. at 500-502.
. Textron's teaching that a court can adjudicate an affirmative defense that the contract was invalid, Textron, 523 U.S. at 658, 118 S.Ct. 1626 (emphasis added), contemplates no distinction between a non-existent contract and a void contract (that was previously existing, i.e., voidable). Contra Jolly Op. at 399.
. While an allegation is sufficient for subject-matter jurisdiction under section 301(a), other statutory provisions impose additional jurisdictional requirements, which are not at issue on this appeal. See 29 U.S.C. 185(c) (personal jurisdiction limitations).
.To be clear, my approach would not preclude a challenge to the factual existence of a labor contract; a court need not assume permanently that a labor contract exists once such existence is alleged. Jolly Op. at 399. However, under Textron, any challenge to such existence would be decided on the merits.
. While the Sixth Circuit in Winnett characterized its own prior holdings as drive-by jurisdictional rulings, Winnett, 553 F.3d at 1005, it did not dismiss the Supreme Court’s prior jurisdictional rulings as equally inconsequential. At least Textron's treatment of section 301(a) as jurisdictional goes well beyond the unrefined dispositions with which the Ar-baugh Court expressed concern. Arbaugh, 546 U.S. at 511, 126 S.Ct. 1235; see also Steel Co., 523 U.S. at 91, 118 S.Ct. 1003 (describing drive-by jurisdictional rulings as cases in which jurisdictional issues were assumed by the parties, and ... assumed without discussion by the Court).
. See ABF Freight System, 645 F.3d at 963 (reviewing Supreme Court case law holding that allegations are sufficient for section 301 jurisdiction, mentioning plaintiffs colorable *405claims of labor contract violation, but also confirming formation of contract as factual matter).
.A jurisdictional test requiring only that a suit originate because a contract has been violated is incompatible with the well-pleaded complaint rule, which Judge Higginson would apply to section 301 actions. Higginson Op. at 419-20 n. 2. Under the well-pleaded complaint rule, courts must look only to the complaint to confirm their jurisdiction. But if a complaint seeking vacatur happens not to mention that the arbitral award arose from an alleged labor contract violation, then a court could examine the award to confirm its jurisdiction.
Furthermore, Textron does not hold that a declaratory-judgment plaintiff who has not alleged the violation of a contract ... therefore [has] not presented] a case or controversy....' Higginson Op. at 420; see also id. at 419-20 n. 2. The case or controversy holding of Textron was premised solely on the unique factual circumstances of the two parties to that action' — there happened to be no evidence that Textron and the union had any concrete dispute over the contract’s voidability at the time when the suit was filed. Textron, 523 U.S. at 660, 661, 118 S.Ct. 1626. The Court even emphasized that it was assuming (without deciding) that a declaratory-judgment complaint raising a nonfederal defense to an anticipated federal claim would confer federal-question jurisdiction under 28 U.S.C. § 1331. Id. at 659, 660, 118 S.Ct. 1626.
. Indeed, the fact that the Textron Court did not bother to discuss either Lingle or Lincoln Mills is telling: The principle common to all three decisions is that a party must allege a labor contract violation in order to invoke section 301(a) jurisdiction.
. See Textron, 523 U.S. at 658, 118 S.Ct. 1626 (holding that [s]ection 301(a) jurisdiction does not lie where plaintiff union sought declaratory judgment that a CBA was voidable).
. See Compl., Appl. to Vacate Arbitration Award & Mem. of Law in Supp. at 8 (claiming that the Union representative, submitted Grievance No. 0-12-09 ..., purportedly under the 2009-12 tentative agreement ... demanding that the Company reinstitute the matching contribution under the 401(k) Plan); id. at 18 (claiming that arbitrator determined, correctly, that the Grievance alleged violations of provisions of the 2009-12 tentative agreement). A plaintiff’s claim that it (and not the defendant) allegedly violated a labor contract is sufficient to support section 301 jurisdiction. See Textron, 523 U.S. at 657, 118 S.Ct. 1626 (‘Suits for violation of contracts’ under § 301(a) are not suits that claim a contract is invalid, but suits that claim a contract has been violated, (emphasis added)); id. at 658, 118 S.Ct. 1626 ([A] declaratory judgment plaintiff accused of violating a collective-bargaining agreement may ask a court to declare the agreement invalid, (emphasis added)).
. See Compl., Appl. to Vacate Arbitration Award & Mem. of Law in Supp. at 18 (Where arbitrators act 'contrary to express contractual provisions,’ they have exceeded their powers.); id. at 22 (alleging that because the dispute over the matching contributions is not subject to the arbitration agreement under the 2006-09 CBA, Arbitrator Griffin exceeded his powers and the Award should be vacated); id. at 26 (alleging that if the 401(k) Plan’s terms are in fact wholly incorporated into the 2006-09 CBA ... then Arbitrator Griffin’s Decision renders Section 11 of the 401(k) Plan meaningless).
. Houston Refining urges us to remand to enable the district court to evaluate independently ... the existence of a CBA. If the district court's subject-matter jurisdiction indeed hinged on a fact-intensive determination, remand would be appropriate. But as explained above, no such factual inquiry is necessary under section 301.
. Indeed, Houston Refining claims in its Statement of Jurisdiction that [t]he lower court had jurisdiction under the LMRA, quoting and citing 29 U.S.C. § 185.
. Although we need not pass on this question today, we express doubt about whether a court can ever assume jurisdiction and proceed to the merits, Montez, 392 F.3d at 150, in light of the Supreme Court's rejection of such hypothetical jurisdiction, Steel Co., 523 U.S. at 94-95, 118 S.Ct. 1003. Read narrowly, our holding in Montez is limited to actions under the Federal Tort Claims Act, Montez, 392 F.3d at 150, but the opinion also refers to the permissibility of hypothetical jurisdiction as the general rule, id. In this observation, Montez relied on Williamson v. Tucker, 645 F.2d 404, 415 (5th Cir.1981). We reserve for a future case a fuller consideration of the correctness of Montez.
. A recent panel of this Court held that it was without statutory ground for appellate jurisdiction under the [Federal Arbitration Act ('FAA')j because the district court neither confirmed nor vacated the arbitration award, but only denied a motion to dismiss and remanded the award to the arbitration panel for clarification of damages. Murchison Capital Partners, L.P. v. Nuance Commc’ns, Inc., No. 13-10852, 760 F.3d 418, 423, 2014 WL 3703868, at *5 (5th Cir. July 25, 2014). We assume (without deciding) that Murchison, decided under the FAA’s provisions governing appellate jurisdiction, 9 U.S.C. § 16(a)(1), governs this appeal in an action under section 301 of the LMRA. Even so, Murchison is distinguishable. There, the panel explained that the district court neither vacated nor confirmed the arbitration award but instead remanded the award back to the arbitration panel for further consideration of damages, and did not dismiss the case, but in fact denied a motion to dismiss. Murchison, 760 F.3d at 420, 422, 2014 WL 3703868, at *2, 4. Here, although the district court remanded the award to the arbitrator for clarification of the remedy, it also granted in substantial part the Union's motion for summary judgment (denying the motion only as to attorney's fees) and concluded that Houston Refining failed to establish ... that the arbitrator’s award should be vacated. Thus, its order confirming an arbitration award is appealable. Id. at 420, 2014 WL 3703868, at *2.
.This judicial deference extends to both the merits of an arbitral award and to an arbitrator’s resolution of procedural preconditions to arbitration. See BG Group PLC v. Republic of Arg., - U.S. -, 134 S.Ct. 1198, 1207, 188 L.Ed.2d 220 (2014). In its reply brief, Houston Refining suggests that EG Group might help clarify whether the grievance’s quotation from the 2009 CBA implicates arbitrability or merely procedural preconditions. We generally do not consider a claim raised for the first time in a reply brief. Cox v. DeSoto Cnty., Miss., 564 F.3d 745, 749 (5th Cir.2009). Additionally, we observe that Houston Refining’s interests would not be served by a determination that the quotation issue implicates mere procedural preconditions under EG Group, since the arbitrator would then be afforded substantial deference on this matter.
. While cases such as First Options arose under the Federal Arbitration Act, courts may rely on this jurisprudence in reviewing arbi-trations under section 301 of the Labor Management Relations Act. Int’l Chem. Workers Union v. Columbian Chems. Co., 331 F.3d 491, 494 (5th Cir.2003). Although Houston Refining is correct that judicial review in these two contexts is not interchangeable, Brabham v. A.G. Edwards & Sons Inc., 376 F.3d 377, 384 (5th Cir.2004), the limited differences are irrelevant to this dispute.
. The district court mistakenly articulated the burden of proof applicable to a party who seeks vacatur of an arbitral award on the merits: As the party seeking to vacate the arbitral award, Houston Refining bears the burden of proof. Here, Houston Refining *409does not challenge the arbitrator’s merits determination that the match suspension violated Article 40; rather, at issue is the procedural question of who decides arbitrability. See First Options, 514 U.S. at 942, 115 S.Ct. 1920 (distinguishing between three issues of merits, arbitrability, and who decides arbitrability). Thus, as the party claiming that the arbitrator has the power to decide arbitrability, the Union — not Houston Refining — bears the initial burden of proving that the parties agreed in sufficiently clear terms to delegate this issue to the arbitrator and thereby take the question away from the courts. ConocoPhiilips, 741 F.3d at 630.
. The parties do not dispute that the 2006 CBA, standing alone, did not manifest an agreement to arbitrate arbitrability.
. The prepositional phrase [a]t arbitration does nothing to resolve the underlying ambiguity. In light of the context of the agreement, Higginson Op. at 421, one could reasonably read the Settlement Agreement to mean that the parties reserve the right to make [any and all] arguments at arbitration, id. at 421. This interpretation, however, relies on repositioning the phrase at arbitration, such that it modifies to present any and all arguments- Settlement Agreement, ¶ 4. But in the actual text of the Settlement Agreement, [a]t arbitration modifies only the main verb phrase shall reserve, which again could be read to mean shall reserve for judicial review. Again, left with two interpretations of the phrase shall reserve, we cannot conclude that the parties clearly and unmistakably agreed to arbitrate arbitrability. ConocoPhiilips, 741 F.3d at 630.
. See also Higginson Op. at 421 (There would have been no need to stipulate to th[e] fact [that the parties could advance 'all arguments and defenses’ at arbitration] in advance if the parties did not intend the arbitrator to decide those questions.).
. To be sure, an arbitration agreement need not recite verbatim that the parties agree to arbitrate arbitrability in order to manifest clear and unmistakable agreement. See, e.g., Petrofac, Inc. v. DynMcDermott Petroleum Operations, 687 F.3d 671, 675 (5th Cir.2012) (concluding that parties agreed to arbitrate arbitrability by incorporating into their arbitration agreement the rules of the American Arbitration Association, which state that [t]he arbitrator shall have the power to rule on his or her own jurisdiction, including any objections with respect to the existence, scope or validity of the arbitration agreement, and reviewing similar cases from sister circuits); Allen v. Regions Bank, 389 Fed.Appx. 441, 446 (5th Cir.2010) (unpublished) (determining that parties clearly agreed to arbitrate arbitra-bility where agreement stated that [a]ny dispute regarding whether a particular controversy is subject to arbitration ... shall be decided by the arbitrator(s)). Furthermore, because the delegation clause granting broad jurisdiction to the arbitrator in Rent-A-Center, W., Inc. v. Jackson, 561 U.S. 63, 130 S.Ct. 2772, 177 L.Ed.2d 403 (2010), did not include any proviso that the parties shall reserve rights to make arguments, that case is inappo-site. See id. at 66, 130 S.Ct. 2772 (explaining that delegation clause provided that Arbitrator ... shall have exclusive authority to resolve any dispute relating to the interpretation, applicability, enforceability or formation of this Agreement (emphasis added)); Higginson Op. at 421-22.
. Article 40 of the 2006 CBA imposes procedural requirements on changes to the 401 (k) Plan:
During the term of this Agreement, the Company will provide advance notice of proposed changes to the benefit plans covered by the Agreement.... A reasonable time period will be provided for the Union to elect inclusion in or exclusion from the amended benefits plan. If the Union elects exclusion, represented employees shall continue participation in the existing, unchanged benefits plan for the term of the Collective Bargaining Agreement.
2006 CBA, art. 40, pt. Ill, ¶ 5.
. See Higginson Op. at 423-24 (applying to arbitrability question here the same deferential review generally applicable to any issue submitted by the parties to the arbitrator).
. Here, I examine the substance of Houston Refining's claim and conclude that it is actually an arbitrability challenge. By contrast, for jurisdictional purposes, I construe the face of Houston Refining’s complaint and conclude that the company does allege that the arbitral award violates the parties' contract by exceeding the arbitrator's mandate. See supra note 17. Of course, a complaint facially alleging only that a dispute was not arbitra-ble would also sufficiently allege a violation of a labor contract — the arbitration of a non-arbitrable dispute violates the scope of powers delegated to the arbitrator.
. Where parties agree to give an issue to the arbitrator, courts apply a deferential standard of review; absent such agreement, courts independently decide the issue. See Schneider v. Kingdom of Thailand, 688 F.3d 68, 72 (2d Cir.2012). Courts must guard against con-flatting] the concepts of deferential and independent review. Id. Although independent *413review also is deferential insofar as courts apply the presumption of arbitrability, Hig-ginson Op. at 423-24 n. 4, the dissent renders meaningless the inquiry into whether parties agreed to arbitrate arbitrability-because either way, a court could ultimately interpret the arbitration clause's scope de novo.
Tellingly, this Court has never found clear and unmistakable agreement to arbitrate ar-bitrability before proceeding to conduct an independent analysis of the arbitration agreement to determine arbitrability. In separating these approaches, we are in the good company of the First, Second, Fourth, Seventh, and Ninth Circuits. Goldman, Sachs & Co. v. City of Reno, 747 F.3d 733, 742 (9th Cir.2014) (undertaking independent review only after determining that parties did not clearly and mistakably agree to arbitrate arbi-trabilily); Peabody Holding Co., LLC v. United Mine Workers of Am., Int’l Union, 665 F.3d 96, 104 (4th Cir.2012) (same); Dialysis Access Ctr., LLC v. RMS Lifeline, Inc., 638 F.3d 367, 376 (1st Cir.2011) (same); R.J. Corman Derailment Servs., LLC v. Int’l Union of Operating Eng’rs, Local Union 150, AFL-CIO, 422 F.3d 522, 527 (7th Cir.2005) (explaining lack of clear and unmistakable agreement to arbitrate arbitrability required court to decide whether the dispute was arbitrable); see also Schneider, 688 F.3d at 74 (concluding that because parties agreed to arbitrate arbitrability, appellant is not entitled to an independent judicial redetermination of that same question). But see Martinez v. Carnival Corp., 744 F.3d 1240, 1246-47 (11th Cir.2014) (undertaking independent review of scope of arbitration clause even after concluding that parties agreed clearly and unmistakably to arbitrate arbitrability).
. To be clear, under the presumption of arbi-trability, we need not reject the dissent’s analysis as legally erroneous or establish a definitively correct interpretation of the 2006 CBA-especially since we decline to decide any arbitration question on this appeal. Rather, we explain below that on the record before us, the case law amply supports at least an interpretation of the 2006 CBA's arbitration clause that favors arbitrability. AT & T, 475 U.S. at 650, 106 S.Ct. 1415 (emphasis added).
. Houston Refining claims that it has made multiple unilateral changes in the past, and that it and the Union have never bargained about any such changes. But Houston Refining and the Union indisputably bargained over the terms of the 2006 CBA, and if that CBA was valid, then the Union would seem to have an actionable right under that CBA, notwithstanding any past failures to enforce that right.
. In fact, those courts concluded that even an arbitration clause covering wages, hours, or working conditions is broad under AT & T, warranting an even stronger presumption of arbitration. See United Steelworks of Am., APL-CIO-CLC v. Rohm & Haas Co., 522 F.3d 324, 331-32 (3d Cir.2008); Printing Specialties & Paper Products Union Local 680, Graphic Commc’n Int’l Union, AFL-CIO v. Nabisco Brands, Inc., 833 F.2d 102, 104 (7th Cir.1987). Our analysis does not depend on this stronger presumption of arbitrability.
. See infra note 39 and accompanying text.
. See Higginson Op. at 425 n. 5 (citing Karl Schmidt Unisia, Inc. v. Int’l Union, United Automobile, Aerospace, & Agric. Implement Workers of Am., UAW Local 2357, 628 F.3d 909, 914-16 (7th Cir.2010); E.I. DuPont De Nemours & Co. v. Ampthill Rayon Workers, Inc., 290 Fed.Appx. 607, 610-12 (4th Cir.2008) (unpublished)).
. See Teamsters Local Union No. 783 v. Anheuser-Busch, Inc., 626 F.3d 256, 258 (6th Cir.2010) (CBA covering all grievances arising under or relating to the interpretation of the CBA); Bridgestone/Firestone, Inc. v. Local Union No. 998, 4 F.3d 918, 923 (10th Cir.1993) (CBA covering disputes over the interpretation or application of [the CBA] or any local plant Supplementary Agreement).
. Besides our Circuit and the Seventh Circuit, the Sixth, Third, Fourth, and Tenth Circuits have also considered the source of the allegedly violated right. Compare Anheuser-Busch, 626 F.3d at 260-63 (holding dispute over individual employee’s pension benefits eligibility not arbitrable, despite broad arbitration clause under AT & T, id. at 261, because the Pension Plan clearly provides a specific mechanism for resolving all grievances related to pension rights, whereby an individual can make a claim for pension benefits to the plan director, id. at 262); Rohm & Haas, 522 F.3d at 332-34 (The employees’ right to receive disability benefits ... derives from the [Health and Welfare] Plan, id. at 334, where CBA d[id] not ... have an article devoted to disability benefits nor [did] it provide any sort of discussion as to the employees’ rights to or calculations regarding such benefits, id. at 332); Bridgestone/Firestone, 4 F.3d at 923 (finding dispute not arbitrable because of separate structure of the two instruments, [and] the absence of any reference to the Suggestion System in the bargaining agreement), with E.I. DuPont de Nemours & Co. v. Ampthill Rayon Workers, Inc., 516 F.Supp.2d 588, 593-94 (E.D.Va.2007) (rejecting employer's claims of potential arbitration-ERISA conflict), aff'd 290 Fed.Appx. 607, 612 (4th Cir.2008) (unpublished) (holding dispute arbi-trable despite potential impact on benefits to employees, given alleged violation of CBA’s procedural rules governing benefit plan amendments); United Steelworkers of Am. v. Mead Corp., Fine Paper Div., 21 F.3d 128, 132 (6th Cir.1994) (holding dispute arbitrable given that union’s claim was governed on its face by the [CBA]).
. Since we do not decide this arbitrability question today, a more considered district court opinion and developed record could inform a future court's analysis. For instance, the record is spare on the CBA’s negotiating history and the Benefits Administrative Committee's authority to apply Article 40 of the 2006 CBA. Regardless of what additional facts and legal arguments are marshalled, Houston Refining cannot carry its burden of overcoming the presumption of arbitrability, Standard Concrete Prods. Inc. v. Gen. Truck Drivers, Office, Food & Warehouse Union, Local 952, 353 F.3d 668, 674 (9th Cir.2003), merely by advancing a reasonable reading of the 2006 CBA. Rather, it must invalidate the Union's interpretation of the CBA’s arbitration clause, such that the CBA is not susceptible of an interpretation that covers the asserted dispute. AT & T, 475 U.S. at 650, 106 S.Ct. 1415 (emphasis added).
. Judge Jolly and Judge Higginson both conclude that jurisdiction is proper, notwithstanding their differing rationales. See supra Part III; Jolly Op. at 398; Higginson Op. Part A. Judge Jolly concurs in the reasoning and holdings in Parts IV and V, while Judge Hig-ginson dissents from both Parts IV and V. See Higginson Op. Parts B, C.